Complex function projective synchronization (CFPS) is the most general synchronization and it enhances the security of communication. However, there always exist unknown parameters for chaotic systems in the real world. Considering all possible cases of unknown parameters of two complex chaotic systems, we design adaptive CFPS schemes and parameters update laws based on speed-gradient (SG) method. The convergence factors and pseudogradient condition are added to regulate the convergence speed and increase robustness. SG method is extended from real field to complex field. Numerical simulations are performed to demonstrate the effectiveness and feasibility of the proposed schemes.